Abstract

Problems associated with the processing and statistical analysis of image data are the subject of much current interest, and many sophisticated techniques for extracting semantic content from degraded or corrupted images have been developed. However, such techniques often require considerable computational resources, and thus are, in certain applications, inappropriate. The detection localised discontinuities, or edges, in the image can be regarded as a pre-processing operation in relation to these sophisticated techniques which, if implemented efficiently and successfully, can provide a means for an exploratory analysis that is useful in two ways. First, such an analysis can be used to obtain quantitative information relating to the underlying structures from which the various regions in the image are derived about which we would generally be a priori ignorant. Secondly, in cases where the inference problem relates to discovery of the unknown location or dimensions of a particular region or object, or where we merely wish to infer the presence or absence of structures having a particular configuration, an accurate edge-detection analysis can circumvent the need for the subsequent sophisticated analysis. Relatively little interest has been focussed on the edge-detection problem within a statistical setting.

In this thesis, we formulate the edge-detection problem in a formal statistical framework, and develop a simple and easily implemented technique for the analysis of images derived from two-region single edge scenes. We extend this technique in three ways; first, to allow the analysis of more complicated scenes, secondly, by incorporating spatial considerations, and thirdly, by considering images of various qualitative nature. We also study edge reconstruction and representation given the results obtained from the exploratory analysis, and a cognitive problem relating to the detection of objects modelled by members of a class of simple convex objects. Finally, we study in detail aspects of one of the sophisticated image analysis techniques, and the important general statistical applications of the theory on which it is founded.